The function $f: \mathbb{Z} \rightarrow \mathbb{Z}$ is called “Sozopolian”, if it satisfies the following two properties: For each two $x,y\in \mathbb{Z}$ which aren’t multiples of 17 the number $f(xy)-f(x)-f(y)$ is divisible by 8; For $\forall x\in \mathbb{Z}$ the number $f(x+17)-f(x)$ is divisible by 8. Does there exist a Sozopolian function for which a) $f(2)=1; \quad$ b) $f(3)=1$?